控制器时滞对磁浮系统稳定性影响分析
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摘要
为研究EMS型磁浮列车悬浮控制器的时滞对磁浮稳定性的影响,解决磁浮列车悬浮不稳的问题,建立了基于双环反馈控制系统的单自由度电磁悬浮模型;以控制器时滞作为参量,通过Routh-Hurwitz稳定性判据判断系统特征根分布,定量给出了系统发生Hopf分岔的时滞临界值,并指出控制器时滞大于临界值时,系统平衡点不再稳定。研制了一种单自由度悬浮试验台,通过数值仿真与台架试验验证了理论分析的正确性。
In order to study the effect of the time delay on the stability of EMS maglev train and solve the problem of instability of maglev train,a single degree of freedom electromagnetic suspension model based on double loop feedback control system was established.Based on the time delay of controller,the Routh-Hurwitz stability criterion was used to determine the characteristic root distribution of the system.The critical threshold of Hopf bifurcation was provided quantitatively.It was pointed out that when the controller delay was larger than the critical value,the system equilibrium point was no longer stable.A singledegree-of-freedom maglev bench was developed.The correctness of the theoretical analysis was verified by numerical simulation and bench test.
In order to study the effect of the time delay on the stability of EMS maglev train and solve the problem of instability of maglev train,a single degree of freedom electromagnetic suspension model based on double loop feedback control system was established.Based on the time delay of controller,the Routh-Hurwitz stability criterion was used to determine the characteristic root distribution of the system.The critical threshold of Hopf bifurcation was provided quantitatively.It was pointed out that when the controller delay was larger than the critical value,the system equilibrium point was no longer stable.A singledegree-of-freedom maglev bench was developed.The correctness of the theoretical analysis was verified by numerical simulation and bench test.
引文
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[9]王洪坡,李杰.一类非自治位置时滞反馈控制系统的亚谐共振响应[J].物理学报,2007,56(5):2504-2516.
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[12]蔡迢阳.基于τ分解方法的几类时滞系统稳定性分析[D].沈阳:东北大学,2016.
[2]梁鑫.磁浮列车车轨耦合振动分析及试验研究[D].成都:西南交通大学,2015.
[3]YABUNO H,KANDA R,LACARBONARA W,et al.Nonlinear active cancellation of the parametric resonance in a magnetically levitated body[J].Journal of Dynamic Systems,Measurement&Control,2004,126(3):433-442.
[4]GOTTZEIN E,BROCK K H,SCHNEIDER E,et al.Control aspects of a tracked magnetic levitation high speed test vehicle[J].Automatica,1977,13(3):205-223.
[5]赵春发,翟婉明.常导电磁悬浮动态特性研究[J].西南交通大学学报,2004,39(4):464-468.
[6]赵春发,翟婉明.低速磁浮车辆导向方式及其横向动态特性[J].中国铁道科学,2005,26(6):28-32.
[7]江浩,连级三.单磁铁悬浮系统的动态模型与控制[J].西南交通大学学报,1992(1):59-67.
[8]邹东升,佘龙华,张志强,等.磁浮系统车轨耦合振动分析[J].电子学报,2010,38(9):2071-2075.
[9]王洪坡,李杰.一类非自治位置时滞反馈控制系统的亚谐共振响应[J].物理学报,2007,56(5):2504-2516.
[10]WANG H P,LI J,ZHANG K.Stability and Hopf bifurcation of the maglev system with delayed speed feedback control[J].Acta Automatica Sinica,2007,33(8):829-834.
[11]张玲玲.磁浮列车悬浮系统的Hopf分岔及滑模控制研究[D].长沙:湖南大学,2011.
[12]蔡迢阳.基于τ分解方法的几类时滞系统稳定性分析[D].沈阳:东北大学,2016.